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Name___________________________________
Unit 1:3
Date: ____________________
N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an
irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
N-CN.1 Know there is a complex number i such that i2 = –1, and every complex # has the form a + bi with a and b real.
N-CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and
multiply complex numbers.
A. Complete the matching
____1. Natural Numbers
B. Is sum or product rational or irrational? Prove it
____2. Whole Numbers
A. a real number that when in decimal
form is infinitely non-repeating
B. i =
____3. Integers
C. { 0, 1, 2, 3, 4, ...}
____4. Rational Numbers
D. can be written in the for a + bi,
where a and b are both real numbers
E. real numbers that when in decimal
form terminate, or infinitely repeat
F. {1, 2, 3, 4, …}
____5. Irrational Numbers
____6. Real Numbers
____7. Imaginary unit
____8. Complex numbers
G. any number that can be written as a
decimal
H. {…-3, -2, -1, 0, 1, 2, 3…}
Rational or Irrational
Product or Sum
Fraction
decimal
1.
_____
_______
_______
2.
_____
_______
______
3.
_____
_______
______
4.
_____
______
______
5.
_____
______
______
6.
______
______
______
C. Indicate whether a rational, irrational or either can be substituted in the blank to get the desired result
1.
2.
3.
4.
5.
6.
D. Answer True or False, if false give an example of how you know
1. Natural numbers are
closed under addition
2. Whole numbers are
closed under subtraction
5. Real numbers are
6. Rational numbers are
closed under subtraction closed under addition
3. Rational numbers are
4. Irrational numbers are
closed under multiplication
closed under addition
7. Irrational numbers are
8. Integers are closed
closed under multiplication
under subtraction
E. Simplify the radical expressions
1.
60
2. 2 64
3.
300
4.
3 49
5.
90
6.
100
7.
25
F. Identify the real and the imaginary number for the complex numbers
1.
Real
2.
______
Imaginary ______
3.
Real
______
Imaginary ______
Real
4.
______
Imaginary ______
5.
Real
______
Imaginary ______
Real
______
Imaginary ______
G. Fill in the table
If the exponent is divisible by _____, i = 1. Match the remainder to the values of i1, i2, i3
Indicate whether the power of i is equal to 1, -1, i, or –i.
1.
2. i 42
3. i 31
4. i 50
5. i 60
H. Simplify and write the expression as a complex number in standard form.
1.  5  2i    3  2i 
2. i   7  5i   3  2  3i 
3.  2  4i    3  9i 
5.
10.
5  2i   2 3  i 
 3  2i 
2
7. i  2  i 
6. 3i  5i 
11. 1  4i 
2
12.  5  4i 
8.
2
 2  3i 1  4i 
13.
7. i 400
6. i 81
7  i 
2
8. i 26
4.  2  4i    3  9i 
9.
 3  7i 1  2i 
14.
 2  7i 
2
I. Two complex numbers a + bi and c + di are equal when a = c and b = d. Solve each for x and y
1. 3x + 4yi = 12 + 8i
2. x + yi = 2 - 3i
3. x + 2yi = 3
4. 2x + yi = 5i
5. x 2yi = 5 + 6i